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Flux Function (flux + function)

Distribution by Scientific Domains
Engineering57%
Mathematics and Statistics42%

Selected Abstracts

Exchange of conserved quantities, shock loci and Riemann problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2001
Michael Sever
Systems of conservation laws admitting extensions, such as entropy density/flux functions, generate related systems obtained by exchanging the extension with one of the constituent equations. Often if not always, the smooth solutions of the two systems coincide, and weak solutions of one system containing only small discontinuities are approximate weak solutions of the other. The adiabatic approximation for the Euler system illustrates the utility of this procedure. Such an exchange of conserved quantities preserves hyperbolicity and genuine non-linearity in the sense of Lax. On the other hand, the topological structure of the shock locus of a point in phase space and the solvability of Riemann problems in the large can be strongly affected. A discussion of when and how this occurs is given here. In this paper the exchange of conserved quantities is conveniently described by a simple homotopy in an extended version of the usual ,symmetric variables'. A dynamical system in phase space is constructed, the trajectories of which describe the Hugoniot locus of a fixed point in phase space at each state of the homotopy. The appearance of critical points for this dynamical system is identified with the alteration of the topological structure of the Hugoniot locus by the exchange of conserved quantities. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Hybrid finite compact-WENO schemes for shock calculation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007
Yiqing Shen
Abstract Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the adjoint solution of the quasi-1D Euler equations: the effect of boundary conditions and the numerical flux function

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005
G. F. Duivesteijn
Abstract This work compares a numerical and analytical adjoint equation method with respect to boundary condition treatments applied to the quasi-1D Euler equations. The effect of strong and weak boundary conditions and the effect of flux evaluators on the numerical adjoint solution near the boundaries are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Solution of the hyperbolic mild-slope equation using the finite volume method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
J. Bokaris
Abstract A finite volume solver for the 2D depth-integrated harmonic hyperbolic formulation of the mild-slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild-slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality-free. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2006
Issam S. Strub
Abstract This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of the boundary conditions is needed for the problem to be well posed. The existence of the solution results from the convergence of the Godunov scheme. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for highway traffic). The numerical scheme is then applied to a highway scenario with data from highway Interstate-80 obtained from the Berkeley Highway Laboratory. Finally, the existence of a minimiser of travel time is obtained, with the corresponding optimal boundary control. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Transport-equilibrium schemes for computing nonclassical shocks.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2008
Scalar conservation laws
Abstract This paper presents a new numerical strategy for computing the nonclassical weak solutions of scalar conservation laws which fail to be genuinely nonlinear. We concentrate on the typical situation of concave,convex and convex,concave flux functions. In such situations the so-called nonclassical shocks, violating the classical Oleinik entropy criterion and selected by a prescribed kinetic relation, naturally arise in the resolution of the Riemann problem. Enforcing the kinetic relation from a numerical point of view is known to be a crucial but challenging issue. By means of an algorithm made of two steps, namely an Equilibrium step and a Transport step, we show how to force the validity of the kinetic relation at the discrete level. The proposed strategy is based on the use of a numerical flux function and random numbers. We prove that the resulting scheme enjoys important consistency properties. Numerous numerical evidences illustrate the validity of our approach. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source]